化简分式：（x+2⼀x+1）-（x+3⼀x+2）+（x-5⼀x-4）-（x-4⼀x-3）

（x+2/x+1）-（x+3/x+2）+（x-5/x-4）-（x-4/x-3）
=[(x+2)²-(x+1)(x+3)]/[(x+1)(x+2)] +[(x-5)(x-3)-(x-4)²]/[(x-4)(x-3)]
=(x²+4x+4-x²-4x-3)/[(x+1)(x+2)] +(x²-8x+15-x²+8x-16)/[(x-4)(x-3)]
=1/[(x+1)(x+2)] -1/[(x-4)(x-3)]
=[(x-4)(x-3)-(x+1)(x+2)]/[(x+1)(x+2)(x-4)(x-3)]
=(x²-7x+12-x²-3x-2)/[(x+1)(x+2)(x-4)(x-3)]
=(-10x+10)/[(x+1)(x+2)(x-4)(x-3)]
=-10(x-1)/[(x+1)(x+2)(x-4)(x-3)]

=[(x+2/x+1)-(x+3/x+2)]+[(x-5/x-4)-(x-4/x-3)]
=[(x+2)(x+2)-(x+3)(x+1)]/(x+1)(x+2)+[(x-5)(x-3)-(x-4)(x-4)]/(x-4)(x-3)
=1/(x+1)(x+2)+(-1)/(x-4)(x-3)
=-10(x-1)/(x+1)(x+2)(x-3)(x-4)
顺便鄙视验证码

10(1-x)/（x-1）（x-2）（x-3）（x-4）

有点难

-2（2x-2)